Pedro F. dos Santos

A note on the equivariant Dold–Thom theorem

Abstract In this note we prove a version of the classical Dold–Thom theorem for the RO( G )-graded equivariant homology functors H ∗ G (−; M ) , where G is a finite group, M is a discrete Z [G] -module, and M is the Mackey functor associated to M . In the case where M= Z with the trivial G -action, our result says that, for a G -CW-complex X , and for a finite dimensional G -representation V , there is a natural isomorphism [S V , Z 0 (X)] G ≅H V G (X; Z ), where Z 0 (X) denotes the free abelian group on X .

ALGEBRAIC CYCLES ON REAL VARIETIES AND Z/2-EQUIVARIANT HOMOTOPY THEORY

In this paper the spaces of algebraic cycles on a real projective variety X are studied as Z/2-spaces under the action of the Galois group Gal(C/R). In particular, the equivariant homotopy type of the group of algebraic p-cycles Zp(PC) is computed. A version of Lawson homology for real varieties is proposed. The real Lawson homology groups are computed for a class of real varieties.

Quaternionic algebraic cycles and reality

In this paper we compute the equivariant homotopy type of spaces of algebraic cycles on real Brauer-Severi varieties, under the action of the Galois group Gal(C/R). Appropriate stabilizations of these spaces yield two equivariant spectra. The first one classifies Dupont/Seymours quaternionic K-theory, and the other one classifies an equivariant cohomology theory 3*(-) which is a natural recipient of characteristic classes KH*(X) → 3*(X) for quaternionic bundles over Real spaces X.

Is prnt a Pseudogene? Identification of Ram Prt in Testis and Ejaculated Spermatozoa

A hallmark of prion diseases or transmissible spongiform encephalopaties is the conversion of the cellular prion protein (PrPC), expressed by the prion gene (prnp), into an abnormally folded isoform (PrPSc) with amyloid-like features that causes scrapie in sheep among other diseases. prnp together with prnd (which encodes a prion-like protein designated as Doppel), and prnt (that encodes the prion protein testis specific - Prt) with sprn (shadow of prion protein gene, that encodes Shadoo or Sho) genes, constitute the “prion gene complex”. Whereas a role for prnd in the proper functioning of male reproductive system has been confirmed, the function of prnt, a recently discovered prion family gene, comprises a conundrum leading to the assumption that ruminant prnt is a pseudogene with no protein expression. The main objective of the present study was to identify Prt localization in the ram reproductive system and simultaneously to elucidate if ovine prnt gene is transcribed into protein-coding RNA. Moreover, as Prt is a prnp-related protein, the amyloid propensity was also tested for ovine and caprine Prt. Recombinant Prt was used to immunize BALB/c mice, and the anti-Prt polyclonal antibody (APPA) immune response was evaluated by ELISA and Western Blot. When tested by indirect immunofluorescence, APPA showed high avidity to the ram sperm head apical ridge subdomain, before and after induced capacitation, but did not show the same behavior against goat spermatozoa, suggesting high antibody specificity against ovine-Prt. Prt was also found in the testis when assayed by immunohistochemistry during ram spermatogenesis, where spermatogonia, spermatocytes, spermatids and spermatozoa, stained positive. These observations strongly suggest ovine prnt to be a translated protein-coding gene, pointing to a role for Prt protein in the ram reproductive physiology. Besides, caprine Prt appears to exhibit a higher amyloid propensity than ovine Prt, mostly associated with its phenylalanine residue.